Let $f:\mathbb{R} \to \mathbb{R}$ be defined by $$f(x) = \frac{{{x^2} – 3x – 6}}{{{x^2} + 2x + 4}}$$ Then which of the following statements is (are) TRUE?
(A) f is decreasing in the interval (-2, -1)
(B) f is increasing in the interval (1, 2)
(C) f is onto
(D) Range of f is $\left[ { – \frac{3}{2},2} \right]$ Continue reading Let $f:\mathbb{R} \to \mathbb{R}$ be defined by ….
There are two columns. Match Column I with appropriate match(es) in Column II. In case you think that there is no suitable match for any particular option then you can say, “None of the match” for that particular option. Your decision to choose a match should not be based on, “may be” but should be based on, “must be”.
Let a, b, c be the sides of triangle ABC.
Continue reading Challenge Problem: Coordinate Geometry/Trigonometry
Previews of all the 17 classes can be seen below.
Evaluate:
$\int\limits_{ – 1}^2 {\left| {{x^3} – x} \right|dx}$
[CBSE 2012]
Solution
Continue reading $$\int\limits_{ – 1}^2 {\left| {{x^3} – x} \right|} dx$$
If the system of equations 2x – y + z =0, x- 2y + z = 0 and ax – y + 2z = 0 has infinitely many solutions and f(x) is continuous function satisfying f(x)+f(x+5) = 2, then $\int\limits_0^{ – 2a} {f(x)dx}$ is equal to
a) 0
b) 5
c) a
d) –2a
Solution
